Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

Abdon Atangana; Seda İğret Araz

doi:10.1186/s13662-021-03213-2

Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

Adv Differ Equ. 2021;2021(1):57. doi: 10.1186/s13662-021-03213-2. Epub 2021 Jan 20.

Authors

Abdon Atangana^{1

2}, Seda İğret Araz³

Affiliations

¹ Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa.
² Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
³ Department of Mathematic Education, Faculty of Education, Siirt University, Siirt, 56100 Turkey.

Abstract

Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented numerous statistical analyses of collected data from both continents using numerous existing statistical theories. Our predictions show the possibility of the second wave of spread in Europe in the worse scenario and an exponential growth in the number of infections in Africa. The projection of statistical analysis leads us to introducing an extended version of the well-blancmange function to further capture the spread with fractal properties. A mathematical model depicting the spread with nine sub-classes is considered, first converted to a stochastic system, where the existence and uniqueness are presented. Then the model is extended to the concept of nonlocal operators; due to nonlinearity, a modified numerical scheme is suggested and used to present numerical simulations. The suggested mathematical model is able to predict two to three waves of the spread in the near future.

Keywords: COVID-19 spread with waves; Extended blancmange function; Modified numerical scheme; Statistical analysis; Stochastic model.